Why is the displacement difference of uniform velocity linear motion in continuous equal time interval a constant

Why is the displacement difference of uniform velocity linear motion in continuous equal time interval a constant

The displacement difference in continuous equal time interval is equal to the difference of average velocity × time uniform motion. The increment of velocity in equal time interval is constant, so the difference of average velocity in continuous equal time interval is constant. Therefore, the displacement difference in continuous equal time interval is a constant, Δ s = Δ V, t = at × t = at